Solve by solving the dual problem. Minimize z = 30x1 + 15x2 + 28x3, subject to 5x1 + 3x2 + 4x3 ≥ 45 5x1 + 6x2 + 8x3 ≥ 120 20x1 + 6x2 + 14x3 ≥ 300 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. x_1= x_2= x_3= z=
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 X1 + X2 + X3 = 1 (a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and...
Consider the following. (x1 - x2 + 4x3 = 20 3x + 332 = -4 -6x2 + 5x3 = 32 (a) Write the system of linear equations as a matrix equation, AX = B. 14 X1 I X2 = IL X3] (b) Use Gauss-Jordan elimination on [ A B] to solve for the matrix X. X2
please show all work, will give good rating. (1 point) Solve the system 5x1-6x2 +2x3 +2x4= 41-5x2 +4x3 44- 2x1 -2x2-4x3-44 aC ac T3 C4
(1 point) Solve the system 5x1 6x2 +7x3 = -3F 15rz- 57 +s
4.3-7. Consider the following problem. Maximize Z = 5x1 + 3x2 + 4x3, subject to 2x1 + x2 + x3<= 20 3x1 + x2 + 2x3 <= 30 and x1 >= 0, x2 >= 0, x3 >= 0. You are given the information that the nonzero variables in the optimal solution are x2 and x3. (a) Describe how you can use this information to adapt the simplex method to solve this problem in the minimum possible number of iterations (when...
Use Cramer's rule to compute the solution of the system. X1 + X2 = 3 - 5x1 + 4x3 = 0 X2 - 4x3 = 2 x1 = 0; x = 0 x3 = 0 (Type integers or simplified fractions.)
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1 + 2x2 –x3= 18, x1 + 3x2+ x3 = 16, has the solution x=(3, 4,2)T. Using the initial guess x (0)=(1, 1,1)T Solve the above system as is using: Gauss-Seidel method. If the error increases, what does that mean and what should you do? (see b below) Condition the system so that convergence is secured and solve using the Gauss-Siedel method. Q2: Find a system...
Consider the function 4X 1X2 + 5x1 + 6x2 + 7, where x = [21, x2]T E R2. Suppose that we use a fixed-step-size gradient algorithm to find the minimizer of f: zo(k+1) = 2(k) – a V f (zo(k)). Find the largest range of value of a for which the algorithm is globally convergent. conv